Frequency estimation for monophonical music by using a modified VMD method

In this paper, a new Variational Mode Decomposition (VMD) is introduced, and applied to the fundamental frequency estimation of monophonical Turkish maqam music. VMD is a method to decompose an input signal into an ensemble of sub-signals (modes) which is entirely non-recursive. It determines the relevant bands adaptively, and estimates the corresponding modes concurrently. In order to optimally decompose a given signal, VMD seeks an ensemble of modes with narrow-band properties corresponding to the Intrinsic Mode Function (IMF) definition used in Empirical Mode Decomposition (EMD). In our proposed modified VMD approach, in order to obtain the bandwidth of a mode, each mode is shifted to baseband by mixing an exponential that is adjusted to the respective center frequency. The bandwidth is estimated through elastic net method that linearly combines penalties of the Lasso and Ridge Regression methods. Simulation results on fundamental frequency estimation of real music and synthetic test data show better performance compared to classical VMD based approach, and other common methods used for music signals, such as YIN and MELODIA based methods.